Numerical experiments for Typhoon Dan incorporating AMSU-A retrieved data with 3DVM

Two sets of assimilation experiments on a landfalling typhoon—Typhoon Dan(1999)over the western North Pacific were designed to compare the performances of two kinds of variational data assimilation schemes that are the 3-Dimensional Variational data assimilation of Mapped observation(3DVM)and the 4-dimensional variational data assimilation(4DVar).Results show that:(1)both the 3DVM and 4DVar successfully improved the simulations of typhoon intensity and track incorporating the satellite AMSU-A retrieved temperature and wind data into the initial conditions,and the 3DVM more significantly due to the flow-dependent of background error covariance matrix and observation error covariance matrix like 3-dimensional variational data assimilation(3DVar)circle;(2)inclusions of extra model integration iterations at each observation time in the 3DVM make it more consistent with prediction model;(3)the 3DVM is much more time-saving due to the exclusion of the adjoint technique in it.     

用一种新的同化方法同化降水量资料

Observations of accumulated precipitation are extremely valuable for effectively improving rainfall analysis and forecast. It is, however, difficult to use such observations directly through sequential assimilation methods, such as three-dimensional variational data assimilation or an Ensemble Kalman Filter. In this study, the authors illustrate a new approach that makes effective use of precipitation data to improve rainfall forecast. The new method directly obtains an optimal solution in a reduced space by fitting observations with historical time series generated by the model; it also avoids the implementation of tangent linear model and its adjoint. A lot of historical samples are produced as the ensemble of precipitation observations with the fully nonlinear forecast model. The results show that the new approach is capable of extracting information from precipitation observations to improve the analysis and forecast. This method provides comparable performance with the standard four- dimensional variational data assimilation at a much lower computational cost.     

A Multivariate Empirical Orthogonal Function-Based Scheme for the Balanced Initial Ensemble Generation of an Ensemble Kalman Filter

The initial ensemble perturbations for an ensemble data assimilation system are expected to reasonably sample model uncertainty at the time of analysis to further reduce analysis uncertainty. Therefore, the careful choice of an initial ensemble perturbation method that dynamically cycles ensemble perturbations is required for the optimal performance of the system. Based on the multivariate empirical orthogonal function (MEOF) method, a new ensemble initialization scheme is developed to generate balanced initial perturbations for the ensemble Kalman filter (EnKF) data assimilation, with a reasonable consideration of the physical relationships between different model variables. The scheme is applied in assimilation experiments with a global spectral atmospheric model and with real observations. The proposed perturbation method is compared to the commonly used method of spatially-correlated random perturbations. The comparisons show that the model uncertainties prior to the first analysis time, which are forecasted from the balanced ensemble initial fields, maintain a much more reasonable spread and a more accurate forecast error covariance than those from the randomly perturbed initial fields. The analysis results are further improved by the balanced ensemble initialization scheme due to more accurate background information. Also, a 20-day continuous assimilation experiment shows that the ensemble spreads for each model variable are still retained in reasonable ranges without considering additional perturbations or inflations during the assimilation cycles, while the ensemble spreads from the randomly perturbed initialization scheme decrease and collapse rapidly.     

Variational data assimilation experiments of mei-yu front rainstorms in China

The numerical forecasts of mei-yu front rainstorms in China has been an important issue. The intensity and pattern of the frontal rainfall are greatly influenced by the initial fields of the numerical model. The 4-dimensional variational data assimilation technology (4DVAR) can effectively assimilate all kinds of observed data, including rainfall data at the observed stations, so that the initial fields and the precipitation forecast can both be greatly improved. The non-hydrostatic meso-scale model (MM5) and its adjoint model are used to study the development of the mei-yu front rainstorm from 1200 UTC 25 June to 0600 UTC 26 June 1999. By numerical simulation experiments and assimilation experiments, the T106 data and the observed 6-hour rainfall data are assimilated. The influences of many factors, such as the choice of the assimilated variables and the weighting coefficient, on the precipitation forecast results are studied. The numerical results show that 4DVAR is valuable and important to mei-yu front rainfall prediction.     

A New Approach to Data Assimilation

A significant attempt to design a timesaving and efficient four-dimensional variational data assimilation (4DVar) has been made in this paper, and a new approach to data assimilation, which is noted as 'three-dimensional variational data assimilation of mapped observation (3DVM)' is proposed, based on the new concept of mapped observation and the new idea of backward 4DVar. Like the available 4DVar, 3DVM produces an optimal initial condition (IC) that is consistent with the prediction model due to the inclusion of model constraints and best fits the observations in the assimilation window through the model solution trajectory. Different from the 4DVar, the IC derived from 3DVM is located at the end of the assimilation window rather than at the beginning conventionally. This change greatly reduces the computing cost for the new approach, which is almost the same as that of the three-dimensional variational data assimilation (3DVar). Especially, such a change is able to improve assimilation accuracy because it does not need the tangential linear and adjoint approximations to calculate the gradient of cost function. Therefore, in numerical test, the new approach produces better IC than 4DVar does for 72-h simulation of TY9914 (Dan), by assimilating the three-dimensional fields of temperature and wind retrieved from the Advanced Microwave Sounding Unit-A (AMSU-A) observations. Meanwhile, it takes only 1/7 of the computing cost that the 4DVar requires for the same initialization with the same retrieved data.     

The REM Adjoint System and Its 4DVar Data Assimilation Experiments

The Regional Eta-coordinate Model(REM) has performed well in forecasting heavy rainfalls in China in recent years.A four-dimensional variational assimilation system(4DVar) is developed to improve the forecast skill of the REM.The tangent linear model and adjoint model codes are written according to thecode to coderule,and the establishment of the REM adjoint modeling system is introduced in detail in this paper.The tangent linear and adjoint models of the REM are validated against the observational data,...     

Idealized Experiments for Optimizing Model Parameters Using a 4D-Variational Method in an Intermediate Coupled Model of ENSO

Large biases exist in real-time ENSO prediction, which can be attributed to uncertainties in initial conditions and model parameters. Previously, a 4 D variational(4 D-Var) data assimilation system was developed for an intermediate coupled model(ICM) and used to improve ENSO modeling through optimized initial conditions. In this paper, this system is further applied to optimize model parameters. In the ICM used, one important process for ENSO is related to the anomalous temperature of subsurface water entrained into the mixed layer(T_e), which is empirically and explicitly related to sea level(SL) variation.The strength of the thermocline effect on SST(referred to simply as "the thermocline effect") is represented by an introduced parameter, αT_e. A numerical procedure is developed to optimize this model parameter through the 4 D-Var assimilation of SST data in a twin experiment context with an idealized setting. Experiments having their initial condition optimized only,and having their initial condition plus this additional model parameter optimized, are compared. It is shown that ENSO evolution can be more effectively recovered by including the additional optimization of this parameter in ENSO modeling.The demonstrated feasibility of optimizing model parameters and initial conditions together through the 4 D-Var method provides a modeling platform for ENSO studies. Further applications of the 4 D-Var data assimilation system implemented in the ICM are also discussed.     

Impact of Analysis-time Tuning on the Performance of the DRP-4DVar Approach

In this study we extend the dimension-reduced projection-four dimensional variational data assimilation (DRP-4DVar) approach to allow the analysis time to be tunable, so that the intervals between analysis time and observation times can be shortened. Due to the limits of the perfect-model assumption and the tangentlinear hypothesis, the analysis-time tuning is expected to have the potential to further improve analyses and forecasts. Various sensitivity experiments using the Lorenz-96 model are conducted to test the impact of analysistime tuning on the performance of the new approach under perfect and imperfect model scenarios, respectively. Comparing three DRP-4DVar schemes having the analysis time at the start, middle, and end of the assimilation window, respectively, it is found that the scheme with the analysis time in the middle of the window outperforms the others, on the whole. Moreover, the advantage of this scheme is more pronounced when a longer assimilation window is adopted or more observations are assimilated.     

Effects of Different Initial Fields on GRAPES Numerical Prediction

In this paper,a heavy rainfall process occurring in the Huaihe River Basin during 9-10 July 2005 is studied by the new generation numerical weather prediction model system-GRAPES,from the view of different initial field effects on the prediction of the model.Several numerical experiments are conducted with the initial conditions and lateral boundary fields provided by T213 L31 and NCEP final analyses,respectively. The sensitivity of prediction products generated by GRAPES to different initial conditions,including effects of three-dimensional variational assimilation on the results,is discussed.After analyzing the differences between the two initial fields and the four simulated results,the memonic ability of the model to initial fields and their influences on precipitation forecast are investigated.Analyses show the obvious differences of sub-synoptic scale between T213 and NCEP initial fields,which result in the corresponding different simulation results,and the differences do not disappear with the integration running.It also shows that for the same initial field whether it has data assimilation or not,it only obviously influences the GRAPES model results in the initial 24 h.Then the differences reduce.In addition,both the Iocation and intensity of heavy rain forecasted by GRAPES model Further is very close to the fact,but the forecasting area of strong torrential rain has some differences from the fact.For the same initial field when it has assimilation, the 9-12-,12-24-,and 0-24-h precipitation forecasts of the model are better than those without assimilation. All these suggest that the ability of GRAPES numerical prediction depends on the different initial fields and lateral boundary conditions to some extent,and the differences of initial fields will determine the differences of GRAPES simulated results.     

EXPERIMENTS OF ENSEMBLE FORECAST OF TYPHOON TRACK USING BDA PERTURBING METHOD

A new method, BDA perturbing, is used in ensemble forecasting of typhoon track. This method is based on the Bogus Data Assimilation scheme. It perturbs the initial position and intensity of typhoons and gets a series of bogus vortex. Then each bogus vortex is used in data assimilation to obtain initial conditions. Ensemble forecast members are constructed by conducting simulation with these initial conditions. Some cases of typhoon are chosen to test the validity of this new method and the results show that: using the BDA perturbing method to perturb initial position and intensity of typhoon for track forecast can improve accuracy, compared with the direct use of the BDA assimilation scheme. And it is concluded that a perturbing amplitude of intensity of 5 hPa is probably more appropriate than 10 hPa if the BDA perturbing method is used in combination with initial position perturbation.     

Sensitivity Experiments of an Eastward-Moving Southwest Vortex to Initial Perturbations

Whether the initial conditions contain pronounced mesoscale signals is important to the simulation of the southwest vortex. An eastward-moving southwest vortex is simulated using the PSU/NCAR MM5. A modest degree of success is achieved, but the most serious failure is that the formation and displacement of the simulated vortex in its early phase are about fourteen hours later than the observed vortex. Considering the relatively sparse data on the mesoscale vortex and in an attempt to understand the cause of the forecast failure, an adjoint model is used to examine the sensitivity of the southwest vortex to perturbations of initial conditions. The adjoint sensitivity indicates how small perturbations of model variables at the initial time in the model domain can influence the vortex. A large sensitivity for zonal wind is located under 400 hPa, a large sensitivity for meridional wind is located under 500 hPa, a large sensitivity for temperature is located between 500 and 900 hPa, and almost all of the large sensitivity areas are located in the southwestern area. Based on the adjoint sensitivity results, perturbations are added to initial conditions to improve the simulation of the southwest vortex. The results show that the initial conditions with perturbations can successfully simulate the formation and displacement of the vortex; the wind perturbations added to the initial conditions appear to be a cyclone circulation under the middle level of the atmosphere in the southwestern area with an anticyclone circulation to its southwest; a water vapor perturbation added to initial conditions can strengthen the vortex and the speed of its displacement.     

IMPACT OF VERTICAL RESOLUTION,MODEL TOP AND DATA ASSIMILATION ON WEATHER FORECASTING——A CASE STUDY

The impacts of stratospheric initial conditions and vertical resolution on the stratosphere by raising the model top, refining the vertical resolution, and the assimilation of operationally available observations, including conventional and satellite observations, on continental U.S. winter short-range weather forecasting, were investigated in this study. The initial and predicted wind and temperature profiles were analyzed against conventional observations. Generally, the initial wind and temperature bias profiles were better adjusted when a higher model top and refined vertical resolution were used. Negative impacts were also observed in both the initial wind and temperature profiles, over the lower troposphere. Different from the results by only raising the model top, the assimilation of operationally available observations led to significant improvements in both the troposphere and stratosphere initial conditions when a higher top was used. Predictions made with the adjusted stratospheric initial conditions and refined vertical resolutions showed generally better forecasting skill. The major improvements caused by raising the model top with refined vertical resolution, as well as those caused by data assimilation, were in both cases located in the tropopause and lower stratosphere. Negative impacts were also observed, in the predicted near surface wind and lower-tropospheric temperature. These negative impacts were related to the uncertainties caused by more stratospheric information, as well as to some physical processes. A case study shows that when we raise the model top, put more vertical layers in stratosphere and apply data assimilation, the precipitation scores can be slightly improved. However, more analysis are needed due to uncertainties brought by data assimilation.     

Evaluating Soil Moisture Predictions Based on Ensemble Kalman Filter and SiB2 Model

Soil moisture is an important variable in the fields of hydrology, meteorology, and agriculture, and has been used for numerous applications and forecasts. Accurate soil moisture predictions on both a large scale and local scale for different soil depths are needed. In this study, a soil moisture assimilation and prediction based on the Ensemble Kalman Filter(EnKF) and Simple Biosphere Model(SiB2) have been performed in Meilin watershed, eastern China, to evaluate the initial state values with different assimilation frequencies and precipitation influences on soil moisture predictions. The assimilated results at the end of the assimilation period with different assimilation frequencies were set to be the initial values for the prediction period. The measured precipitation, randomly generated precipitation,and zero precipitation were used to force the land surface model in the prediction period. Ten cases were considered based on the initial value and precipitation. The results indicate that, for the summer prediction period with the deeper water table depth, the assimilation results with different assimilation frequencies influence soil moisture predictions significantly. The higher assimilation frequency gives better soil moisture predictions for a long lead-time. The soil moisture predictions are affected by precipitation within the prediction period. For a short lead-time, the soil moisture predictions are better for the case with precipitation, but for a long lead-time, they are better without precipitation. For the winter prediction period with a lower water table depth, there are better soil moisture predictions for the whole prediction period. Unlike the summer prediction period, the soil moisture predictions of winter prediction period are not significantly influenced by precipitation. Overall, it is shown that soil moisture assimilations improve its predictions.     

A Comparison Study of Tropical Pacific Ocean State Estimation： Low-Resolution Assimilation vs. High-Resolution Simulation

A comparison study is performed to contrast the improvements in the tropical Pacific oceanic state of a low-resolution model respectively via data assimilation and by an increase in horizontal resolution.A low resolution model (LR) (1°lat by 2°lon) and a high-resolution model (HR) (0.5°lat by 0.5°lon) are employed for the comparison. The authors perform 20-yr numerical experiments and analyze the annual mean fields of temperature and salinity. The results indicate that the low-resolution model with data assimilation behaves better than the high-resolution model in the estimation of ocean large-scale features.From 1990 to 2000, the average of HR's RMSE (root-mean-square error) relative to independent Tropical Atmosphere Ocean project (TAO) mooring data at randomly selected points is 0.97℃ compared to a RMSE of 0.56℃ for LR with temperature assimilation. Moreover, the LR with data assimilation is more frugal in computation. Although there is room to improve the high-resolution model, the low-resolution model with data assimilation may be an advisable choice in achieving a more realistic large-scale state of the ocean at the limited level of information provided by the current observational system.     

Dynamical and Microphysical Retrieval from Simulated Doppler Radar Observations Using the 4DVAR Assimilation Technique

Based on a cloud model and the four-dimensional variational (4DVAR) data assimilation method developed by Sun and Crook (1997), simulated experiments of dynamical and microphysical retrieval from Doppler radar data were performed. The 4DVAR data assimilation technique was applied to a cloud scale model with a warm rain parameterization scheme. The 3D wind, thermodynamical, and microphysical fields were determined by minimizing a cost function, defined by the difference between both radar observed radial velocities and reflectivities and their model predictions. The adjoint of the numerical model was used to provide the gradient of the cost function with respect to the control variables. Experiments have demonstrated that the 4DVAR assimilation method is able to retrieve the detailed structure of wind, thermodynamics, and microphysics by using either dual-Doppler or single-Doppler information. The quality of retrieval depends strongly on the magnitude of constraint with respect to the variables. Retrieving the temperature field, cloud water and water vapor is more difficult than the recovery of the wind field and rainwater. Accurate thermodynamic retrieval requires a longer assimilation period. The inclusion of a background term, even mean fields from a single sounding, helped reduce the retrieval errors. Less accurate velocity fields were obtained when single-Doppler data were used. It was found that the retrieved velocity is sensitive to the location of the retrieval domain relative to the radars while the other fields have very little changes. Two radar volumetric scans are generally adequate for providing the evolution, although the use of additional volumes improves the retrieval. As the amount of the observations decreases, the performance of the retrieval is degraded. However, the missing observations can be compensated by adding a background term to the cost function. The technique is robust to random errors in radial velocity and calibration errors in reflectivity. The boundary conditions from the dual-Doppler synthesized winds are sufficient for the retrieval. When the retrieval is mainly controlled by the observations in the regions away from the boundaries, the simple boundary conditions from velocity azimuth display (VAD) analysis are also available. The microphysical retrieval is sensitive to model errors.     

Impact of 4DVAR assimilation of rainfall data on the simulation of mesoscale precipitation systems in a mei-yu heavy rainfall event

The multi-scale weather systems associated with a mei-yu front and the corresponding heavy precipitation during a particular heavy rainfall event that occurred on 4 5 July 2003 in east China were successfully simulated through rainfall assimilation using the PSU/NCAR non-hydrostatic, mesoscale, numerical model （MM5） and its four-dimensional, variational, data assimilation （4DVAR） system. For this case, the improvement of the process via the 4DVAR rainfall assimilation into the simulation of mesoscale precipitation systems is investigated. With the rainfall assimilation, the convection is triggered at the right location and time, and the evolution and spatial distribution of the mesoscale convective systems （MCSs） are also more correctly simulated. Through the interactions between MCSs and the weather systems at different scales, including the low-level jet and mei-yu front, the simulation of the entire mei-yu weather system is significantly improved, both during the data assimilation window and the subsequent 12-h period. The results suggest that the rainfall assimilation first provides positive impact at the convective scale and the influences are then propagated upscale to the meso- and sub-synoptic scales.
Through a set of sensitive experiments designed to evaluate the impact of different initial variables on the simulation of mei-yu heavy rainfall, it was found that the moisture field and meridional wind had the strongest effect during the convection initialization stage, however, after the convection was fully triggered, all of the variables at the initial condition seemed to have comparable importance.     

Impact of 4DVAR Assimilation of AIRS Total Column Ozone Observations on the Simulation of Hurricane Earl

The Atmospheric Infrared Sounder(AIRS) provides twice-daily global observations of brightness temperature, which can be used to retrieve the total column ozone with high spatial and temporal resolution.In order to apply the AIRS ozone data to numerical prediction of tropical cyclones, a four-dimensional variational(4DVAR) assimilation scheme on selected model levels is adopted and implemented in the mesoscale non-hydrostatic model MM5. Based on the correlation between total column ozone and potential vorticity(PV), the observation operator of each level is established and five levels with highest correlation coefficients are selected for the 4DVAR assimilation of the AIRS total column ozone observations. The results from the numerical experiments using the proposed assimilation scheme for Hurricane Earl show that the ozone data assimilation affects the PV distributions with more mesoscale information at high levels first and then influences those at middle and low levels through the so-called asymmetric penetration of PV anomalies.With the AIRS ozone data being assimilated, the warm core of Hurricane Earl is intensified, resulting in the improvement of other fields near the hurricane center. The track prediction is improved mainly due to adjustment of the steering flows in the assimilation experiment.     

A MODEL OF INTEGRATED RANDOM INITIAL VALUES AND RANDOM FORCING AND ITS PRELIMINARY EXPERIMENT

A simple quasi-geostrophic barotropic vorticity equation model is used as the dynamic frame of themodel in this paper.Considering that there are many random errors in model's initial values of meteorolo-gical data,and that it is not perfectly complete about model's physical processes (for example,take no ac-count of the interaction between atmosphere and underlying surface,radiation,etc.),we add the random for-ced term to the model and use the Monte-Carlo method with random initial values.A statistical-dynamicintegrated model is thus built up,and a numerical forecasting experiment of 500hPa monthly mean height fieldof January 1983 has been carried out.The experiment result proves that the forecasting result of the model,considering random forcing and random initial values at the same time,is better than that by the pure dynamicmodel,the random initial value model and the random forced model.     

Adjoint sensitivity study on idealized explosive cyclogenesis

The adjoint sensitivity related to explosive cyclogenesis in a conditionally unstable atmosphere is investigated in this study.The PSU/NCAR limited-area,nonhydrostatic primitive equation numerical model MM5 and its adjoint system are employed for numerical simulation and adjoint computation,respectively.To ensure the explosive development of a baroclinic wave,the forecast model is initialized with an idealized condition including an idealized two-dimensional baroclinic jet with a balanced three-dimensional moderateamplitude disturbance,derived from a potential vorticity inversion technique.Firstly,the validity period of the tangent linear model for this idealized baroclinic wave case is discussed,considering different initial moisture distributions and a dry condition.Secondly,the 48-h forecast surface pressure center and the vertical component of the relative vorticity of the cyclone are selected as the response functions for adjoint computation in a dry and moist environment,respectively.The preliminary results show that the validity of the tangent linear assumption for this idealized baroclinic wave case can extend to 48 h with intense moist convection,and the validity period can last even longer in the dry adjoint integration.Adjoint sensitivity analysis indicates that the rapid development of the idealized baroclinic wave is sensitive to the initial wind and temperature perturbations around the steering level in the upstream.Moreover,the moist adjoint sensitivity can capture a secondary high sensitivity center in the upper troposphere,which cannot be depicted in the dry adjoint run.     

Estimating the Soil Moisture Profile by Assimilating Near-Surface Observations with the Ensemble Kalman Filter （EnKF）

The paper investigates the ability to retrieve the true soil moisture profile by assimilating near-surface soil moisture into a soil moisture model with an ensemble Kalman filter （EnKF） assimilation scheme, including the effect of ensemble size, update interval and nonlinearities in the profile retrieval, the required time for full retrieval of the soil moisture profiles, and the possible influence of the depth of the soil moisture observation. These questions are addressed by a desktop study using synthetic data. The ＂true＂ soil moisture profiles are generated from the soil moisture model under the boundary condition of 0.5 cm d^-1 evaporation. To test the assimilation schemes, the model is initialized with a poor initial guess of the soil moisture profile, and different ensemble sizes are tested showing that an ensemble of 40 members is enough to represent the covariance of the model forecasts. Also compared are the results with those from the direct insertion assimilation scheme, showing that the EnKF is superior to the direct insertion assimilation scheme, for hourly observations, with retrieval of the soil moisture profile being achieved in 16 h as compared to 12 days or more. For daily observations, the true soil moisture profile is achieved in about 15 days with the EnKF, but it is impossible to approximate the true moisture within 18 days by using direct insertion. It is also found that observation depth does not have a significant effect on profile retrieval time for the EnKF. The nonlinearities have some negative influence on the optimal estimates of soil moisture profile but not very seriously.